Simplify; express your answer in exponential form. Assume $p\neq 0, x\neq 0$. $\dfrac{{(p^{2})^{2}}}{{(p^{-2}x^{-4})^{5}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{2}}$ to the exponent ${2}$ . Now ${2 \times 2 = 4}$ , so ${(p^{2})^{2} = p^{4}}$ In the denominator, we can use the distributive property of exponents. ${(p^{-2}x^{-4})^{5} = (p^{-2})^{5}(x^{-4})^{5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{2})^{2}}}{{(p^{-2}x^{-4})^{5}}} = \dfrac{{p^{4}}}{{p^{-10}x^{-20}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{4}}}{{p^{-10}x^{-20}}} = \dfrac{{p^{4}}}{{p^{-10}}} \cdot \dfrac{{1}}{{x^{-20}}} = p^{{4} - {(-10)}} \cdot x^{- {(-20)}} = p^{14}x^{20}$.